System for characterizing a light field

ABSTRACT

A method and system for establishing extended optical traps for commercial use. The method and system employs a diffractive optical element (DOE) to process a light beam wherein the DOE includes phase information and amplitude information to create the extended optical trap. Such extended traps can be line traps and can be further expanded to two and three dimensional configurations.

CROSS-REFERENCE TO RELATED PATENT APPLICATIONS

This application is a continuation and claims priority from copendingU.S. patent application Ser. No. 11/633,178, filed Dec. 4, 2006, whichclaims priority from U.S. Provisional Patent Application No. 60/742,444,filed Dec. 5, 2005, U.S. Provisional Patent Application No. 60/777,622,filed Feb. 28, 2006 and U.S. Provisional Patent Application No.60/852,252 filed Oct. 17, 2006 incorporated herein by reference in theirentirety.

This invention was made with U.S. Government support under Grant No.DMR-0451589 awarded by the National Science Foundation. The U.S.Government has certain rights in this invention.

FIELD OF THE INVENTION

The present invention relates generally to a system and method forcontrollably establishing extended optical traps for processingmaterials for a wide variety of uses. More particularly the inventionrelates to the use of shape-phase modulation or holography to establisha variety of shapes of optical traps, such as lines, curves and threedimensional shapes for manipulating, orienting, manufacturing andprocessing of objects ranging from nanoscale to micrometer scaleobjects.

BACKGROUND OF THE INVENTION

Various attempts have been made in the prior art to extend a singlepoint-like optical trap into lines, curves and three dimensional shapes,but serious deficiencies are inherent in all such efforts. For example,line tweezers have been implemented with a cylindrical lens or itsholographic equivalent. A line formed with a cylindrical lens isdegraded by severe astigmatism, however, and therefore cannot trapobjects in three dimensions. A cylindrical lens also cannot produce moregeneral structures, only linear extended traps. Line traps also havebeen formed with pairs of cylindrical lenses arranged in a Kepleriantelescope. Although such line traps can be free from astigmatism, theirshape is fixed, and their intensity and phase profiles cannot bealtered. Such line traps also are incompatible with the holographicoptical trapping technique, and therefore cannot be integrated with thevariety of trapping capabilities made possible by holographicprojection. In another prior art methodology extended optical traps havebeen created by time sharing or scanning of optical traps. This methodsuffers from various disadvantages described in detail hereinafter.

In yet another prior art methodology extended optical traps can beprojected by conventional holographic techniques. This approach does notallow for general three dimensional structures for the projected lineand suffers from projection deficiencies, such as optical speckle.Further disadvantages will be described hereinafter as part of thedescription of this invention, thus demonstrating the substantialadvantages over the prior art.

SUMMARY OF THE INVENTION

A single-beam optical gradient force trap can be generalized toestablish its domain of influence along a specified curve or volume witha predetermined intensity to define lines and volumes of optical trapinfluence. Such an extended trap and the attendant domain of influencecan be generated by use of shape-phase modulation or holography. Thiscan furthermore extend to projecting a plurality of such traps. Extendedoptical traps can for example be implemented for one-dimensionalpotential energy wells to manipulate nanometer scale to micrometer-scaleobjects. Trapping one, two, or more such objects in a single, tailoredand well-characterized extended potential energy well has numerousapplications in process monitoring, quality control, process control andnanomanufacturing, as well as in research and other fields.

The simplest extended optical trap takes the form of a so-called linetweezer, in which an appropriately structured beam of light focuses to asegment of a line, rather than to a spot. Such line tweezers have beenimplemented with a cylindrical lens, or with its holographic equivalent.The resulting trap has some undesirable characteristics, however. A linetrap projected with a cylindrical lens actually has thethree-dimensional structure of a conventional optical tweezer degradedby severe astigmatism. Consequently, it focuses to a line along one axisin one plane and to a perpendicular line in another plane. The two linescross on the beam's axis, which decreases axial intensity gradients atthat point, and thus severely degrades such traps' ability to trapobjects in three dimensions. Cylindrical lenses also can project only asingle line tweezer, and offer no control over the intensity and phaseprofiles along the line. Finally, cylindrical lenses can only projectlinear extended traps, and not more general structures. The systemdescribed hereinafter avoids these shortcomings by allowing for thecreation of one or more extended traps, each of which focuses to asingle curve on a specified trapping manifold, and each of which has anindependently specified intensity and phase profile along its length.

In the prior art, extended optical traps also have been created in atime-shared sense by scanning a single optical tweezer rapidly acrossthe field of view. Provided the tweezer travels rapidly enough, atrapped object cannot keep up with the tweezer, but rather experiencesan extended potential whose characteristics reflect a time average ofthe tweezer's transit. This has the disadvantage that high peak laserpowers are required to maintain even a modest average well depth, andthis can degrade light-sensitive samples. The scanned laser also canimpart transient energy or impulses to briefly illuminated objects,which can result in subtle yet undesirable nonequilibrium effects.Finally, scanned optical tweezers typically operate in only a singleplane and not along more general curves in three dimensions. The systemdescribed here avoids these drawbacks by offering continuousillumination over its entire length of the projected traps. Such asystem also offers the ability to project extended optical traps alongthree-dimensional curves, as will be illustrated in the sectionshereinafter.

Extended optical traps might also be projected by conventionalholographic methods. In this case, a phase-only or amplitude-onlyhologram encoding the desired curve is projected into a sample. Mostsuch holograms, however, do not specify the three-dimensional structureof the projected line, and thus do not optimize the intensity gradientsnecessary for optical trapping in all three dimensions. Conventionalholographic line traps also suffer from projection deficiencies such asspeckle. These alter the intensity distribution along the projectedcurve in such a way as to degrade the intended potential energy wellstructure. Because the phase transfer function encoding such aholographic line trap is related in an intrinsically nonlinear manner tothe intensity pattern that is projected, optimizing to correct forprojection deficiencies is difficult. The system described herein avoidsthese difficulties by encoding both phase and amplitude information inthe shape of a phase hologram, as well as in its phase values. Theresult is a specific, smoothly varying trapping pattern that can beadaptively optimized. For example, the trap in a preferred embodiment isbest extended along a line perpendicular to an optical axis andvirtually any light distribution intensity or phase profile can beimposed along the line. Such light illumination can be continuous alongthe selected line (or curve as explained hereinafter) such that a lowintensity can be used thereby avoiding sample damage. These types ofextended traps can be created or established by a conventionalholographic trap system provided the appropriate phase and amplitudehologram is utilized. These extended line traps can also be used withadditional trapping modalities, such as optical vortices, which can bemixed with extended optical traps with each modality defined by aspecific operation on the wavefronts of the light designed to implementa new functionality.

These and other objects, advantages, and features of the invention,together with the organization and manner of operation thereof, willbecome apparent from the following detailed description when taken inconjunction with the accompanying drawings, wherein like elements havelike numerals throughout the several drawings described below.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates a schematic diagram of an optical trap used toproject extended optical traps;

FIG. 2 illustrates a phase mask function encoding a uniformally brightline tweezer;

FIG. 3A illustrates a calculated intensity pattern; FIG. 3B illustratesan experimental pattern; and FIG. 3C illustrates the extended opticaltraps aligning and trapping seven polystyrene spheres of 1.5 fromdiameter and dispersed in water;

FIG. 4A illustrates a Gaussian calculation for imaging photograph ofholographic line tweezers longitudinal and transverse intensity profiles(circles); the inset is an image of the projected light and FIG. 4Bbeing the measured potential energy well for a 1.5 micrometer diameterpolystyrene spheres in water at 1.5 mW laser power and the dashed lineshows a parabolic fit; FIG. 4C is a uniform line calculation with theprojected light onset; FIG. 4D is a bright field image of the sevenspheres trapped on the line; and FIG. 4E is a double-well flat-topprofile calculation and with the projected light inset;

FIG. 5 illustrates another system for projecting an extended opticaltrap with a computer generated hologram;

FIG. 6A illustrates a three dimensional reconstruction of an opticaltweezer propagating along the axis; FIG. 6B shows a cross section in thexy phase; FIG. 6C shows a cross section in the yz phase with thehorizontal dashed line indicating the phase z=z_(o) in which its xysection is obtained and FIG. 6D shows a cross section in the xz phasewith the inset isosurface enclosing 95% of the incident light; and thescale bar in FIG. 6C is indicative of 5 micrometers and the crosssections in each plane are gray scale intensity level for the insetscale in FIG. 6D;

FIG. 7A illustrates a volumetric representation of 35 optical tweezerarranged in the body centered cubic lattice of FIG. 7B;

FIGS. 8A-8D illustrate reconstruction of a cylindrical line tweezer andshould be compared with FIG. 6A-6D as their respective counterparts; and

FIG. 9A-9D illustrates a three dimensional sequential reconstruction ofa holographic optical line trap in accordance with an embodiment of theinvention and should be compared with FIGS. 6A-6D and 8A-8D.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

FIG. 1 schematically represents a typical optical train or system 90that can be used to project extended optical traps. A laser 100 projectsa beam of light 110 to an objective lens 120, which focuses the beaminto an optical trap within a sample 130. Typically, a beam expander 140is required so that the diameter of the beam matches the input apertureof the focusing lens 120 to form the strongest possible optical trap. Inthis implementation, a dichroic mirror 150 is shown reflecting the laserbeam 110 into the objective lens 120. This permits images to be createdof objects interacting with the trap, the imaging light passing throughthe dichroic mirror 150. In a typical implementation, imaging light canbe focused onto the sample 130 by a condenser lens 200, collected by theobjective lens 120, and relayed to a camera 210 by an eyepiece 220.

If there were no additional functionality, this system 90 would projecta single conventional optical tweezer. The addition of an appropriatelyconfigured diffractive optical element (DOE) 300 and additional relayoptics 310 enables the system 90 to project extended optical traps. Themost preferred DOE 300 in FIG. 1 is a spatial light modulator (SLM),which is a device capable of encoding the pattern of phase modulationdefining a diffractive optical element, typically under computercontrol. An SLM form of the DOE 300 is particularly useful when asequence of trap-forming holograms is to be projected, but is notnecessary for practice of the present invention. In otherimplementations where a single pattern of extended optical traps isrequired, a static form of the DOE 300 can be substituted for the SLM.This system 90 already has been shown to be useful for projectingholographic optical traps (HOTs), and can be used to project severalclasses of extended optical traps in addition to the class underdiscussion here. Specifically, holographic optical traps can projectoptical vortices, which are ring-like optical traps that exert torque aswell as force. The HOT technique also can be used to project generalizedoptical vortices whose curve of maximum intensity can fall along anarbitrary specified curve. Optical vortices and their generalizationshave two principal drawbacks: the torque they exert cannot beeliminated, and is not desirable for all applications, and theirintensity profile cannot be specified. HOTs also can project Besselbeams, which are one-dimensional axial line traps. These, however, arelimited to forming line traps along the optical axis, they exert forcesalong their length, and their intensity profile cannot be specified.Finally, the HOT technique also can project cylindrical line traps andholographic line traps, both of which suffer from the implementationalproblems discussed hereinbefore.

An extended line trap differs from these other types of holographicoptical traps in the nature of the DOE 300 used to project it. Inparticular, projecting extended traps requires encoding both phase andamplitude information in the hologram, whereas conventional holographicoptical traps require only phase information. We encode both phase andamplitude information in a phase-only DOE by specifying the shape of thedomain within the DOE 300 over which phase information is encoded. Theuse of phase information to create extended optical traps is oneparticularly useful embodiment. In the following paragraphs we explainthe principle of shape-phase modulation or shape-phase holography andits application to creating extended optical traps with specified shapesand force profiles. As a concrete example, we present the implementationof a uniform line tweezer. Further, we describe methods for modifyingthe trap's outline from a line segment in the plane to a more generalcurve in three dimensions for volumetric applications.

An ideal line tweezer focuses to a line segment with a specifiedintensity distribution and has the steepest possible intensity gradientsin all directions perpendicular to the line. This can be achieved inprinciple by inverting the mathematical relationship between light inthe lens' focal volume and the electric field in the plane of the DOE300. The result generally involves modulating both the amplitude andphase of the incoming light, which is not possible given the DOE 300that modulates only phase or only amplitude. The key point in thepresent invention is that a line tweezer is inherently one-dimensional,and thus both its amplitude and phase information can be encoded in atwo-dimensional phase-only DOE 300 by using one dimension to encodephase information and the transverse dimension to encode amplitudeinformation.

As an example, we form a uniformly bright line tweezer of length Laligned with the ŷ axis in the lens' focal plane. The field in thetrapping plane may be approximated as

$\begin{matrix}{{\Psi(r)} = \left\{ \begin{matrix}{{\delta(x)},} & {{y} < \frac{L}{2}} \\{0,} & {otherwise}\end{matrix} \right.} & (1)\end{matrix}$

The inverse Fourier transform of this field yields the associated fieldin the DOE plane;

$\begin{matrix}{{{\Psi(\rho)} = {{\sin\;{c\left( {k\;\rho_{y}} \right)}} = \frac{\sin\left( {k\;\rho_{y}} \right)}{k\;\rho_{y}}}},{{{where}\mspace{14mu} k} = \frac{\pi}{L}},} & (2)\end{matrix}$

which is a purely real-valued function. Because Ψ(ρ) involves onlyamplitude modulations and has both negative and positive values, itmight not seem possible to encode it on a phase-only DOE 300. However,Ψ(ρ) does not depend on ρ_(x), and this presents the opportunity onwhich shape-phase modulation is based.

We rewrite the input field as:Ψ(ρ)=A(ρ)exp(iφ(ρ)),  (3)

where A(ρ) is a positive definite amplitude and φ(ρ) is a real-valuedphase. By inspection of Eq. (2),A(ρ)=|sin c(kρ _(y))|  (4)

and, noting that

$\begin{matrix}{{{\varphi(\rho)} = {\frac{\pi}{2}\left\lbrack {1 + {{sgn}\left( {\sin\;{c\left( {k\;\rho_{y}} \right)}} \right)}} \right\rbrack}}{where}} & (5) \\{{{sgn}(x)} = \left\{ \begin{matrix}{1,} & {x > 0} \\{0,} & {x = 0} \\{- 1} & {x < 0}\end{matrix} \right.} & (6)\end{matrix}$

If we assume that the DOE 300 is uniformly illuminated, thenA(ρ)=A(ρ_(x)) may be interpreted as the fraction of light incident onthe DOE at ρ_(y) that is allowed to pass through to form the trap. For apixellated DOE, this corresponds to the fraction of the pixels along therow at ρ_(y) that contribute to the hologram. Light passing through theother pixels does not contribute to the hologram, and must be divertedaway from the projected pattern. The resulting division of the inputfield into regions that contribute to the hologram and regions that donot constitutes the shape component of shape-phase holograms. It isworth emphasizing that A(ρ) is independent of ρ_(x) for any linear trapaligned along ŷ, and φ(ρ) are both independent of ρ_(x) for the specialcase of a uniformly bright line. Consequently, the amplitude functionA(ρ_(y)) specifies how many pixels at ρ_(y) contribute to the hologram,but not which pixels contribute. This offers additional latitude forcreating multiple line traps and for combining line traps with othertrapping modalities, as we will show below.

For the uniform line tweezer, therefore, one appropriate phase functionis

$\begin{matrix}{{\varphi(\rho)} = \left\{ \begin{matrix}{{\frac{\pi}{2}\left\lbrack {1 + {{sgn}\left( {\sin\;{c\left( {k\;\rho_{y}} \right)}} \right)}} \right\rbrack},} & {{\rho_{x}} < {\frac{1}{2}{A\left( \rho_{y} \right)}}} \\{unassigned} & {otherwise}\end{matrix} \right.} & (7)\end{matrix}$

Light passing through the unassigned region ordinarily would be broughtto a focus in the middle of the focal plane, where it would contributeto forming a conventional optical tweezer. Alternately, the light can bediverted away from the line by imposing a conventional displacing phasefunction:

$\begin{matrix}{{{\varphi(\rho)} = {{{q \cdot \rho_{1}}\mspace{14mu}{for}\mspace{14mu}{\rho_{x}}} \geq {\frac{1}{2}{A\left( \rho_{y} \right)}}}},} & (8)\end{matrix}$

where q is a constant wavevector describing the unassigned light'sdisplacement. Such a displacement function accounts for the scallopedbackground in the DOE phase function 400 in FIG. 2. Here, a smoothgradient along {circumflex over (ρ)}_(x) is wrapped around at a phasevalue of 2π to create an equivalent sawtooth phase function. The linetweezer also can be displaced away from the optical axis by adding aphase function of the form of Eq. (8) to the assigned pixels. Lightpassing through the unassigned pixels still can be diverted to anotherdirection by selecting a different value of q for the unassigned pixels.

The extra light also can be dispersed by assigning random phase valuesto the unassigned phase pixels. Finally, the extra light can be used toconstruct additional line tweezers. This extra functionality requiresthe line traps to be displaced relative to the optical axis so that theydo not overlap. The unassigned region also can be applied to otherapplications such as creating conventional optical tweezers, opticalvortices, and other optical trapping modalities.

For example, a uniform line tweezer can be projected with

$\begin{matrix}{{{\varphi_{s}(\rho)} = {{\varphi\left( \rho_{y} \right)}{S(\rho)}}},{where}} & (9) \\{{S(\rho)} = \left\{ \begin{matrix}{1,} & {{\rho_{x}} < {A\left( \rho_{y} \right)}} \\{0,} & {otherwise}\end{matrix} \right.} & (10)\end{matrix}$The shape function S(ρ) divides the plane of the DOE into assigned (S=1)and unassigned (S=0) regions. Light passing through the unassignedregion can be diverted, diffused, or applied to another task by applyinganother phase mask, φ_(1-S)(ρ), to the unassigned pixels. Light passingthrough the assigned region then has both the phase and amplitudestructure needed to form the extended optical trap.

FIG. 2 shows a phase-only hologram that encodes a uniform line tweezerL=15 μm long according to Eq. (9) and uses the unassigned pixels toproject a conventional optical tweezer displaced laterally by 50micrometers. The calculated intensity pattern, shown in FIG. 3A, agreesclosely with the actual light distribution measured by placing a mirrorin the sample plane and collecting the reflected light with theobjective lens, FIG. 3B.

The line trap 410 in FIG. 2 suffers from three easily remedied defects.The analytical shape function described by Eq. (10) creates transverseartifacts at the line's ends. These are eliminated by replacing S(ρ)with a random distribution that assigns the correct number of pixels ineach column. The abrupt intensity gradients called for in Eq. (3)furthermore exceed a practical DOE's spatial bandwidth, and so causeoscillatory deviations from the designed intensity profile. This is anexample of Gibbs phenomenon, which can be minimized by modifying thetrap's design to reduce gradients, or through standard numericalmethods. The results in FIG. 4A-4E show the benefits of thesecorrections.

When powered by 15 mW of light, each of these line tweezers readilytraps micrometer-scale colloidal spheres in three dimensions, whileallowing them some freedom of motion along the extended axis. Wecharacterized the extended traps' potential energy profiles for 1.5 μmdiameter polystyrene spheres (Duke Scientific Lot 5238) by placing asingle particle on the line and tracking its thermally driven motions at1/30 sec intervals and 10 nm spatial resolution through digital videomicroscopy. The probability P(r)d²r to find the particle within d²r ofposition r in equilibrium is related to the local potential V(r) byBoltzmann's equation,P(r)=exp(−βV(r)),  (11)where β⁻¹=k_(B)T is the thermal energy scale at absolute temperature T.A single particle's trajectory over ten minutes yields the results inFIG. 4A. The longitudinal potential energy profile closely follows thedesigned shape and is 30±7 k_(B)T deep. The bottom third of the well isplotted in FIG. 4A together with a fit to a parabolic profile.Deviations from the designed shape are smaller than 0.8 k_(B)T. Thesecould be further reduced by adaptive optimization. The transverseprofile is broadened by the sphere's diameter, as expected.

This system 90 shown in FIG. 1 was preferably used to implement the linetrap 410. Here the phase function 400 incorporates the shape-phasehologram described by Eq. (7) and displaces the unassigned light usingEq. (8). As shown in FIG. 3A, both an extended line trap 412 and thediverted tweezer 414 are shown in an intensity distribution calculatedfor this phase function 400. Results showing the experimental version ofthe line trap 412 and the diverted tweezer 414 projected in practice areshown in the photograph of FIG. 3B. This line trap 412 is sixteenmicrometers long. The inset photograph of FIG. 3C shows this extendedoptical trap trapping seven polystyrene spheres, each 1.5 micrometers indiameter, dispersed in water.

Other modifications to the phase mask 400, which have been described inapplications apart from the invention herein, can be used to translatethe line tweezer along the optical axis, to correct for aberrations inthe system 90, and to account for such defects in the system 90 as phasescaling errors.

Unlike line traps created with cylindrical lenses, or their equivalent,this shape-phase holographic line trap 410 is not simply astigmatic, butrather has the three-dimensional structure of an extended cone. Thisstructure is ideal for optical trapping because it yields the strongestpossible axial intensity gradients. Consequently, it successfully trapsobjects along its length without intercession of a substrate or othersources of force.

Multiple extended optical traps can be projected with the same DOEprovided their shape functions S_(j)(ρ) are disjoint in the sense that∫_(Ω)S_(i)(ρ)S_(j)(ρ)d²ρ=0 for i≠j. The assigned domain then isS(ρ)=Σ_(j)S_(j)(ρ). Other modifications to the phase mask 400 that havebeen described in other contexts can be used to translate the line trap410 along the optical axis, to correct for aberrations in the opticaltrain, and to account for such defects in the optical train as phasescaling errors. Finally, the shape-phase modulation can be generalizedfor intensity modulation of curved tweezers by applying an appropriateconformal mapping to the phase mask 400.

The shape-phase modulation can be generalized for intensity modulationof curved tweezers. For this we identify a curve in the reciprocallattice that is projected into the desired curved tweezer or trap.Modulation of intensity of the reciprocal curve result in modulation ofthe intensity over the curved tweezer. In order to achieve the desiredmodulation, the shape in the normal direction to the curve is set by theamplitude function while the phase of each segment along this line isdetermined by the phase of the quasi one-dimensional equivalent problem(similarly for the line shape-phase modulation). This results in a twodimensional curved tweezer or trap.

Addition of a phase function or the mask 400 that can be described by aconformal mapping (e.g a distorted lens phase) can bend this line into athree dimensional curve, and result in three dimensional extended trap.The resulting conformal mapping mask can be included only in theamplitude shape area (e.g a cylindrical lens phase can help modify thewidth of a line trap), or can cover all of the phase mask 400 (e.g aradial phase can shift the focus plane from the central spot). Thus amixed shape-phase modulation and conventional phase modulation can beapplied together to form a mixed modulation mode.

Extension of Optical Traps to Three Dimensions

In the following a detailed view is provided of extended optical traps'three-dimensional intensity distributions which can be created andcompared with other classes of extended optical traps.

These embodiments are based on a preferred optimized holographictrapping technique, shown schematically in FIG. 5. Here, a beam of laserlight 500 from a frequency-doubled solid-state laser (not shown)(Coherent Verdi) operating at a wavelength of λ=532 nm is directedthrough relay optics 505 to the input pupil of a high-numerical-apertureobjective lens 510 (Nikon 100× Plan Apo, NA 1.4, oil immersion) thatfocuses it into an optical trap. The laser beam 500 is imprinted with aphase-only hologram by a computer-addressed liquid-crystal spatial lightmodulator 520 (SLM, Hamamatsu X8267 PPM) in a plan conjugate to theobjective's input plan. As a result, the light field, ψ(r), in theobjective's focal plan is related to the field ψ(r), in the objective'sfocal plan is related to the field ψ(p) in the plane of the SLM 520 bythe well known Fraunhofer transform:

$\begin{matrix}{{{\psi(r)} = {{- \frac{\mathbb{i}}{\lambda\; f}}{\int_{\Omega}^{\;}{{\psi(\rho)}{\exp\left( {{- {\mathbb{i}}}\;\frac{2\pi}{\lambda\; f}{r \cdot \rho}} \right)}{\mathbb{d}{\,^{2}\rho}}}}}},} & (12)\end{matrix}$where f is the objective's focal length, where Ω is the optical train'saperture, and where we have dropped irrelevant phase factors. Assumingthat the laser illuminates the SLM 520 with a radially symmetricamplitude profile, u(ρ), and uniform phase, the field in the SLM's planemay be written asψ(ρ)=u(ρ)exp(iφ(ρ)),  (13)where φ(ρ) is the real-valued phase profile imprinted on the laser beam500 by the SLM 520. The SLM 520 in our system imposes phase shiftsbetween 0 and 2π radians at each pixel of a 768×768 array. Thistwo-dimensional phase array can be used to project a computer-generatedphase-only hologram, φ(ρ), designed to transform the single opticaltweezer into any desired three-dimensional configuration of opticaltraps, each with individually specified intensities and wavefrontproperties.

Ordinarily, the pattern of holographic optical traps would be put to useby projecting it into a fluid-borne sample mounted in the objective'sfocal plane. To characterize the light field, we instead mount afront-surface mirror in the sample plane. This mirror reflects thetrapping light back into the objective lens 510, which transmits imagesof the traps through a partially reflecting mirror 540 to acharge-coupled device (CCD) camera 530 (NEC TI324AII). In ourimplementation, the objective lens 510, camera eyepiece are mounted in aconventional optical microscope (Nikon TE-2000U).

Three-dimensional reconstructions of the optical traps' intensitydistribution can be obtained by translating the mirror 540 relative tothe objective lens 510. Equivalently, the traps can be translatedrelative to fixed mirror 550 by superimposing the parabolic phasefunction.

$\begin{matrix}{{{\varphi_{z}(\rho)} = {- \frac{\pi\;\rho^{2}z}{\lambda\; f^{2}}}},} & (14)\end{matrix}$onto the hologram φ₀(ρ) encoding a particular pattern of traps. Thecombined hologram, φ(ρ)=φ₀(ρ)+φ_(x)(ρ) mod 2π, projects the same patternof traps as φ₀(ρ) but with each trap translated by −z along the opticalaxis. The resulting image obtained from the reflected light represents across-section of the original trapping intensity at distance z from theobjective's focal plane. Translating the traps under software control isparticularly convenient because it minimizes changes in the opticaltrain's properties due to mechanical motion. Images obtained at eachvalue of z are stacked up to yield a complete volumetric representationof the intensity distribution.

The objective lens 510 captures essentially all of the reflected lightfor z≦0. For z>0, however, the outermost rays of the converging trap arecut off by the objective's output pupil, and the contrast is reducedaccordingly. This could be corrected by multiplying the measuredintensity field by a factor proportional to z for z>0. The appropriatefactor, however, is difficult to determine accurately, so we presentonly unaltered results.

FIGS. 6A-6D shows a conventional optical tweezer reconstructed in thisway and displayed as an isointensity surface at 5 percent peak intensityand in three cross-sections. The former is useful for showing theover-all structure of the converging light, and the cross-sectionsprovide an impression of the three dimensional light field that willconfine an optically trapped object. The angle of convergence of 63° inimmersion oil obtained from these data is consistent with an overallnumerical aperture of 1.4. The radius of sharpest focus, r_(min)≈0.2micrometers, is consistent with diffraction-limited focusing on thebeam.

These results highlight two additional aspects of this reconstructiontechnique. The objective lens 510 is designed to correct for sphericalaberration when light passing through water is refracted by a glasscoverslip. Without this additional refraction, the projected opticaltrap actually is degraded by roughly 20λ of spherical aberration,introduced by the objective lens 510. This reduces the apparentnumerical aperture and also extends the trap's focus along the z axis.The trap's effective numerical aperture in water would be roughly 1.2.The effect of spherical aberration can be approximately corrected bypre-distorting the beam with the additional phase profile,

$\begin{matrix}{{{\varphi_{a}(\rho)} = {\frac{a}{\sqrt{2}}\left( {{6x^{4}} - {6x^{2}} + 1} \right)}},} & (15)\end{matrix}$

The Zernike polynomial describes spherical aberration. The radius, x, ismeasured as a fraction of the optical train's aperture, and thecoefficient a is measured in wavelengths of light. This procedure isused to correct for small amount of aberration present in practicaloptical trapping systems to optimize their performance.

This correction was applied to the array of 35 optical tweezers shown asa three-dimensional reconstruction in FIGS. 7A and 7B. These opticaltraps of FIG. 7A are arranged in a three-dimensional body-centered cubic(BCC) lattice of FIG. 7B with a 10.8 micrometer lattice constant.Without correcting for spherical aberration, these traps would blendinto each other along the optical axis. With correction, their axialintensity gradients are clearly resolved. This accounts for holographictraps' ability to organize objects along the optical axis.

The amount of spherical aberration caused by projecting into immersionoil rather than water is so large that the combination of φ_(z)(ρ) andφ_(n)(ρ) can exceed the spatial bandwidth of the SLM 520 for all but thesimplest trapping patterns, φ_(o)(ρ). We therefore provide more complextraps without aberration correction. In particular, we used uncorrectedvolumetric imaging to illustrate the comparative advantages of extendedoptical traps created by recently introduced holographic techniques.

Extended optical traps have been projected in a time-shared sense byrapidly scanning a conventional optical tweezer along the trap'sintended contour. A scanned trap has optical characteristics as good asa point-like optical tweezer, and an effective potential energy wellthat can be tailored by adjusting the instantaneous scanning rate.Kinematic effects due to the trap's motion can be minimized by scanningrapidly enough. For some applications, however, continuous illuminationor the simplicity of an optical train with no scanning capabilities canbe desirable.

Continuously illuminated line traps have been created by expanding anoptical trap along one direction. This can be achieved, for example, byintroducing a cylindrical lens into the objective's input plane.Equivalently, a cylindrical-lens tweezer can be implemented by encodingthe function φ_(c)(ρ)=πz₀ρ² _(x)/(λ∫²) on the SLM 520. The results,shown in FIGS. 8A-8D appear serviceable in the plane of best focus,z=z_(o), with the point-like tweezer having been extended to a line witha nearly uniform intensity profile and parabolic phase. Thethree-dimensional reconstruction in FIG. 8A, however, reveals that thecylindrical lens merely introduces a large amount of astigmatism intothe beam, creating a second focal line perpendicular to the first. Thisis problematic because the astigmatic beam's intensity gradients areseverely weakened along the optical axis compared with a conventionaloptical tweezer. Consequently, cylindrical lens line traps typicallycannot localize objects against radiation pressure along the opticalaxis.

Replacing the single cylindrical lens with a cylindrical Kepleriantelescope eliminates the astigmatism and thus creates a stablethree-dimensional optical trap. Similarly, using an objective lens tofocus two interfering beams creates an interferometric optical trapcapable of three-dimensional trapping. These approaches, however, offerlittle control over the extended traps' intensity profiles, and neitheraffords control over the phase profile.

Shape-phase holography provides absolute control over both the amplitudeand phase profiles of an extended optical trap at the expense ofdiffraction efficiency. It also yields traps with optimized axialintensity gradients, suitable for three-dimensional trapping. If theline trap is characterized by an amplitude profile u(ρ_(x)) and a phaseprofile p(ρ_(x)) along the ρ_(x) direction in the objective's focalplan, then the field in the SLM plane is given by Eq. (12) asψ(ρ)=u(ρ_(x))exp(ip(ρ_(x))),  (16)Where the phase p(ρ_(x)) is adjusted so that u(ρ_(x))>0. Shape-phaseholography implements this one-dimensional complex wavefront profile asa two-dimensional phase-only hologram

$\begin{matrix}{{\varphi(\rho)} = \left\{ \begin{matrix}{{p\left( \rho_{x} \right)},} & {{\rho \in {S(\rho)}},} \\{{q(\rho)},} & {\rho \notin {S(\rho)}}\end{matrix} \right.} & (17)\end{matrix}$Where the shape function S(ρ) allocates a number of pixels along the rowρ_(y) proportional to u(ρ_(x)). One particularly effective choice is forS(ρ) to select pixels randomly along each row in the appropriaterelative numbers. The unassigned pixels then are given values q(p) thatredirect the excess light away from the intended line. Typical resultsare presented in FIGS. 9A-9D.

Unlike the cylindrical-lens trap, the holographic line trap focuses as aconical wedge to a single diffraction limited line in the objective'sfocal plane. Consequently, its transverse angle of convergence iscomparable to that of an optimized point trap. This means that theholographic line trap has comparably strong axial intensity gradients,which explains its ability to trap objects stably against radiationpressure in the z direction.

The line trap's transverse convergence does not depend strongly on thechoice of intensity profile along the line. Its three-dimensionalintensity distribution, however, is very sensitive to the phase profilealong the line. Abrupt phase changes cause localized suppression of theline trap's intensity through destructive interference. Smoothervariations do not affect the intensity profile along the line, but cansubstantially restructure the beam. The line trap created by acylindrical lens, for example, has a parabolic intensity profile andalso a parabolic phase profile. Inserting this choice into Eq. 13 andcalculating the associated shape-phase hologram with Eqs. (12) and (17)yields the idealized cylindrical lens phase transfer function. Thisobservation opens the door to applications in which the phase profilealong a line can be tuned to create a desired three-dimensionalintensity distribution, or in which the measured three-dimensionalintensity distribution can be used to assess the phase profile along theline.

Numerous uses are contemplated using the extended optical traps forchemical, mechanical, electrical and biological processing of materials,including without limitation manipulation, probing, selected chemicaland biological reaction, testing, manufacture and assembly of materials.In one example use, functionalized spheres (or any type of particle ormass) can be positioned along a line established as an extended opticaltrap. Such assemblies or particles can also be probed and reacted andinteractions between and among particles readily ascertained. Inaddition nanowires can be readily manipulated, probed and processedusing extended traps. Particle or nanowires or other mescopic materialcan be disposed in programmable potential wells of such extended trapsto measure interactions and character of the trapped material.Measurements are also easily performed under such well established onedimensional states which can be formed, rather than having todeconvolute information from more complicated two and three dimensionalarrangements of particles or material. Both similar and dissimilarmaterials can be probed by means of extended optical traps andcorrections for optical perturbations or other complications can readilybe effectuated using extended optical trap formalisms. These techniqueshave a wide array of applications for physical, chemical, electronic,mechanical, optical, and biological systems. In addition extendedoptical traps can be utilized for manufacturing and assembly purposesdue to their programmable nature and flexibility. In chemical,biological and electrical applications such extended traps can be usedto programmably react materials, assemble macromolecules, electroniccircuits and create nanoscale biological media not previouslyachievable. In the area of manufacturing and processing, a phase onlypattern can be imposed along a line or curve wherein the intensityremains constant but the optical force can be programmed to any profileallowing movement, acceleration and deceleration which can be part of ananomanufacturing assembly or production line. In yet another examplemicrofluidic systems can be constructed and operated using extendedoptical traps.

It should be understood that various changes and modifications referredto in the embodiment described herein would be apparent to those skilledin the art. Such changes and modifications can be made without departingfrom the spirit and scope of the present invention.

1. A system for characterizing a light field to be used for at least oneof manipulation, manufacturing, orienting, analyzing or processing ofmaterial, comprising: a light source to provide a light beam; an opticalelement to process the light beam, the optical element including phaseinformation and amplitude information to create a light field; an objectlens disposed to process the light beam containing the light field; asample plane determined by the objective lens focal plane; and a frontsurface mirror disposed in the sample plane for reflecting the lightbeam containing the light field back into the objective lens, therebyenabling transmission of images of the light field to a camera foranalysis.
 2. The system as defined in claims 1 wherein the material isdisposed in a sample plane.
 3. The system as defined in claim 2 whereinthe light field comprises an optical trap.
 4. The system as defined inclaim 3 wherein the optical trap comprises an extended optical trap. 5.The system as defined in claim 1 wherein the front surface mirrorincludes a partially reflecting mirror disposed between the objectivelens and the camera.
 6. The system as defined in claim 5 furtherincluding a mechanical drive to translate a moveable form of thepartially reflecting mirror, thereby reconstructing intensitydistribution of the light field.
 7. The system as defined in claim 5wherein the partially reflecting mirror comprises a fixed mirror and thelight field is translated by the diffractive optical element, therebyreconstructing intensity distribution of the light field.
 8. The systemas defined in claim 7 wherein a parabolic phase function is superimposedonto the light field to enable translating the light field.
 9. Thesystem as defined in claim 6 wherein the parabolic phase functioncomprises,${\Phi_{z}(\rho)} = {- {\frac{\pi\;\rho^{2}z}{\lambda\; f^{2}}.}}$ 10.The system as defined in claim 1 wherein the objective lens isconstructed to correct for spherical aberration in the light beam andthe resulting light field.
 11. The system as defined in claim 1 whereinthe optical element comprises a diffractive optical element.
 12. Thesystem as defined in claim 1 wherein the images comprise a 3Dreconstructed image.
 13. A system for characterizing a light field to beused for interacting with a material disposed in a sample plane,comprising: a light source to provide a light beam; a diffractiveoptical element to process the light beam, the diffractive opticalelement including phase information and amplitude information of thelight field; an object lens disposed to process the light beamcontaining the light field; a sample plane determined by the objectivelens focal plane; and a front surface mirror disposed in the sampleplane for reflecting the light beam containing the light field back intothe objective lens, thereby enabling transmission of images to a camerafor analysis and use in interacting with the material.
 14. The system ofclaim 13, wherein the light field represents at least one holographicoptical trap.
 15. The system of claim 14, wherein the phase informationand amplitude information are encoded to create an extended opticaltrap, the extended optical trap represented by the light field containedin the light beam reflected by the front surface mirror and the imagestransmitted being images of the extended optical trap.